Optical metrology techniques generally referred to as scatterometry offer the potential to characterize parameters of a workpiece during a manufacturing process. In practice, light is directed onto a periodic grating formed in a workpiece and spectra of reflected light is measured and analyzed to characterize the grating parameters. Characterization parameters may include critical dimensions (CD), sidewall angle (SWA), feature height (HT), etc. which effect a material's reflectivity and refractive index. Characterization of the grating may thereby characterize the workpiece as well as a manufacturing process employed in the formation of the grating and the workpiece. For example, optical metrology system 100 depicted in FIG. 1A can be used to determine the profile of a grating 102 formed on a semiconductor wafer 104. Grating 102 can be formed in test areas on wafer 104, such as adjacent to a device formed on wafer 104. The optical metrology system 100 can include a photometric device with a source 106 and a detector 112. Grating 102 is illuminated by an incident beam 108 from source 106. In the present exemplary embodiment, incident beam 108 is directed onto grating 102 at an angle of incidence θi with respect to normal of grating 102 and an azimuth angle φ (i.e., the angle between the plane of incidence of beam 108 and the direction of the periodicity of grating 102). Diffracted beam 110 leaves at an angle of θd with respect to normal and is received by detector 112. Detector 112 converts the diffracted beam 110 into a measured metrology signal. To determine the profile of grating 102, optical metrology system 100 includes a processing module 114 configured to receive the measured metrology signal and analyze the measured metrology signal.
Analysis of measured spectra generally involves comparing the measured sample spectra to simulated spectra to deduce a model's parameter values that best describe the measured sample. FIG. 1B illustrates a method 100 for a building parameterized model and a spectra library beginning with sample spectra (e.g., originating from one or more workpieces). At operation 102, a set of material files are defined by a user to specify characteristics (e.g., n, k values) of the material(s) from which the measured sample feature is formed.
At operation 102, a scatterometry user defines a nominal model of the expected sample structure by selecting one or more of the material files to assemble a stack of materials corresponding to those present in the periodic grating features to be measured. This user-defined model may be further parameterized through definition of nominal values of model parameters, such as thicknesses, CD, SWA, HT, edge roughness, corner rounding radius, etc. which characterize the shape of the feature being measured. Depending on whether a 2D model (i.e., a profile) or 3D model is defined, it is not uncommon to have 30-50, or more, such model parameters.
From a parameterized model, simulated spectra for a given set of grating parameter values may be computed using rigorous diffraction modeling algorithms, such as Rigorous Coupled Wave Analysis (RCWA). Regression analysis is then performed at operation 106 until the parameterized model converges on a set of parameter values characterizing a final profile model (for 2D) that corresponds to a simulated spectrum which matches the measured diffraction spectra to a predefined matching criterion. The final profile model associated with the matching simulated diffraction signal is presumed to represent the actual profile of the structure from which the model was generated.
The matching simulated spectra and/or associated optimized profile model can then be utilized at operation 107 to generate a library of simulated diffraction spectra by perturbing the values of the parameterized final profile model. The resulting library of simulated diffraction spectra may then be employed by a scatterometry measurement system operating in a production environment to determine whether subsequently measured grating structures have been fabricated according to specifications.
Library generation 107 may include a machine learning system, such as a neural network, generating simulated spectral information for each of a number of profiles, each profile including a set of one or more modeled profile parameters. In order to generate the library, the machine learning system itself may have to undergo some training based on a training data set of spectral information. Such training may be computationally intensive and/or may have to be repeated for different models and/or profile parameter domains. Considerable inefficiency in the computational load of generating a library may be introduced by a user's decisions regarding the size of a training data set. For example, selection of an overly large training data set may result in unnecessary computations for training while training with a training data set of insufficient size may necessitate a retraining to generate a library.
An automated method for determining a size of a training data set would therefore be advantageous.